Disaster Prevention Education Handout using
Mathematics for Junior High School Students
CountryAgeName

1. Root
When xn = a，x is defined the nth root of a．
【example】 Second root (square root) of 4 is 2．

Third root (cube root) of 27 is 3．
Fourth root of 16 is 2．
· When n is an even number,√√a > 0 ⇒ There are two nth roots，and they are expressed n a，− n a．
a < 0 ⇒ There is no nth root of a．

· When n is an odd number，√Regardless the sign of a，there’s one nth root of a，expressed n a．
√√
【example】 4 is the second root of 4，so 4 = 2．
([Attention] When you think about the second root of a，it is expressed√
omit the subscript of root，2，not 2 a．)√√
3
8 is the third root of 8，so 3 8 = 2．
√√√√
3− 4 = −2，−4 = No exist，−8 = −2， − 3 −8 = 2√

a，Question 1 Find the value．
(1)
(5)

√9=

√
416 =

(2)

√

−9 =

√
(6) 4 −16 =√(3) 3 27 =√(4) 3 −27 =√(7) − 4 16 =√(8) − 4 −16 =Speed of TsunamiThe speed of tsunami V (km/h) in the depth of water h(m) is given by the following formula．
√
V = 3.6 9.8h
Question2 Find the value of tsunami speed for the following depth of water．
(1) The deepest depth in ; Lake Hamana : 16 (m)(2) The deepest depth in ; Tokyo Bay : 70 (m)(3) The deepest depth in ; Toyama Bay : 1,200 (m)(4) The deepest depth in ; Suruga Bay : 2,500 (m)Height of Tsunami (Green’s Law)In one oﬀshore，when the hight of wave is H1 (m)，the depth of water is h1 (m)，the hight ofwave near the coast is H(m)，the depth of water is h(m)，H is given by the next formula．
√H = 4 hh1 × H1
At the Meteorological agency，the hight of wave near the coast is defined “h = 1(m)”．
Question3 Find the height of wave near the coast for the following two situations．
(1) The water depth and wave height are 16(m) and 1(m)．
(2) The water depth and wave height are 100(m) and 2(m)．
2. Logarithm
When a > 0, a ̸= 1, and the following equation ⃝1 was right, m is defined Logarithm in the basea. In adddition, m is expressed by the following equation ⃝.
2
am = N · · · ⃝1m = loga N · · · ⃝2

The relation between index and logarithm

am = N ⇔ m = loga N

22 = 4，2 = log2 4． 23 = 8，3 = log2 8．

eg )log2 32 = 5，log3 9 = 2，log3 27 = 3
Question4 Find the following values．
(1) log2 64 =(2) log4 16 =(3) log5 125 =(4) log10 10 =(5) log10 100 =(6) log10 105 =The relation between energy from earthquake and magnitude（Richter scale）



When the energy from earthquake is E(J)，the magnitude is M ，E is expressed by the following
formula．
log10 E = 4.8 + 1.5M

namely，E = 104.8+1.5M

Question5
Find the values of earthquake energy of M 7，M 8 and M 9．Then，find how many times theearthquake energy multiple when the magnitude increases by 1 and 2．
When M 7，E =When M 8，E =When M 9，E =

3. Trigonometric ratio
In three sides of right triangle ABC (Hypotenuse，Adjacent，Opposite)，the two line ratios oflength from an acute angle A are written as sinA, cosA, and tanA．These are defined like the next
expressions．sinA, cosA, and tanA are pronounced as sineA, cosineA, and tangentA. They arecalled Trigonometric ratio.
OppositeBCB
sin A ==

Hypotenuse
AB
Hypotenuse
AC
Adjacent
Opposite cos A = Hypotenuse = ABOppositeBCAtan A ==Adjacent
ACAC
Adjacent【example】
Trigonometric ratio of angle A and B of following right triangle are written in next values．

 AA5
B

B

3

C

4

3
54
cos A =
53
tan A =
4

4
53
cos B =
54
tan B =
3

sin A =

sin B =

【example】
Trigoronometric ratio of angle A and B of following right triangle are written in next values using
Pythagoras’ theorem．
1
sin A = √
10B
3


cos A = √

10


2


1
tan A =
 A
3AC
6

Question6 Find the trigonometric ratio of angle A for following figures．
(2)

(1)

!
!!
!
!
!! A!
13!!
!!

12!
!!
5A


sin A =

5
sin A =

cos A =

cos A =tan A =tan A =

√
5 3

Question7 Find the trigonometric ratio of the following figures．

◦
30






60◦
45◦

sin 30◦ =sin 45◦ =sin 60◦ =cos 30◦ =cos 45◦ =cos 60◦ =tan 30◦ =tan 45◦ =tan 60◦ =Question8 When you were looking out to the sea after an earthquake，the tsunami wave wasappering at the horizon．The distance of the shore to the horizon is 4000(m)．Find the nextvalues．
(1) When you were looking up to the height of the tsunami ，the angle of elevation was 0.1◦ ．
Find the opposite of the height of tsunami at the horizon，by refering the following figure andtable．

((((((((((((((◦
0.1((((((((((((((((((((Opposite of wave

4000m(※ Fig1. Tsunami wave height，angle and distance from shore to the horizon．)[Attention]
You must run away from the sea after an earthquale as soon as you can to keep your life !
angle
0.1◦
0.2◦
0.3◦
0.4◦
0.5◦
0.6◦
0.7◦
0.8◦
0.9◦
1.0◦sin0.001745
0.003491
0.005236
0.006981
0.008727
0.010471
0.012217
0.013962
0.015707
0.017452

cos
0.999998
0.999993
0.999986
0.999976
0.999962
0.999945
0.999925
0.999902
0.999877
0.999848tan
0.001745
0.003491
0.005236
0.006981
0.008727
0.010472
0.012218
0.013963
0.015709
0.017455(2) When the depth of water near the shore was 1(m) and the depth of water at the horizon was
1000(m)，find the height of the tsunami when it arrived near the shore．